Advertisement

Maintaining a Cultural Identity While Constructing a Mathematical Disposition as a Pāsifika Learner

  • Roberta HunterEmail author
  • Jodie Hunter
Living reference work entry

Abstract

Many Pāsifika students enter New Zealand schools fluent in their own language and with a rich background of knowledge and experiences. But, within a short period of schooling they join the disproportionately high numbers of Pāsifika students who are failing subjects such as mathematics within our current education system. The reasons are diverse but many can be attributed directly to the structural inequities they encounter which cause a disconnect (and dismissal) of their Indigenous cultural values, understandings, and experiences.

In this chapter, we examine and explore the different practices which have marginalized Pāsifika students in our schools and more specifically in mathematics classrooms. We explain how some of the “taken-as-granted” practices in mathematics classrooms match the cultural capital of the dominant middle-class students but position Pāsifika students in ways which cause them cultural dissonance. What we clearly show is that the teaching and learning of mathematics cannot ignore the student’s culture despite the beliefs held by many that mathematics is “culture-free.” In contrast, we illustrate that the teaching and learning of mathematics is wholly cultural and is closely tied to the cultural identity of the learner. We provide many examples over 15 years that illustrate that when teachers use pedagogy situated within the known world of their Pāsifika students and which premise student choice over their spoken language their sense of belonging within schools is affirmed. We draw on the voices of the Pāsifika students to show how Pāsifika-focused culturally responsive teaching has the potential to address issues of equity and social justice which supports them retaining their cultural identity while constructing a positive mathematical disposition.

Keywords

Culturally responsive teaching Cultural identity Mathematical disposition Equity Social justice 

Introduction

Within New Zealand’s polyethnic society, Pāsifika peoples hold an important place. Pāsifika as a term has come to describe Indigenous peoples from other Pacific Island nations who live in Aotearoa New Zealand. In the post–second world war industrial era and into more recent times, their contributions, both economically and politically, have helped shape New Zealand as we know it today. Equally important are the Pāsifika ancestral links with Māori, the Indigenous people of New Zealand. In addition, the rich and colorful elements Pāsifika peoples bring to New Zealand add to the cultural landscape of this country. Currently, there are less than 10% of students of Pāsifika ethnic origin attending New Zealand schools. Wylie (2003) indicates a doubling of these numbers by the year 2051, and Brown and colleagues (2007) signal that Pāsifika students are the fastest growing population in New Zealand schools. However, appropriate institutional and policy-driven responses have been slow to acknowledge, respect, and incorporate core Pāsifika goals and values. One of the major consequences of this, as many researchers (Alton-Lee 2003; Bills and Hunter 2015; Nakhid 2003; Wendt-Samu 2006; Young-Loveridge 2009) have documented, is the disproportionate number of Pāsifika students who perform well below the desired levels in comparison to their Pākehā (Māori term commonly used to refer to European New Zealanders) and Asian counterparts in mathematics and literacy. Our aim in this chapter is to explore how Pāsifika students are able to develop a strong mathematical identity as they simultaneously engage in mathematical activity which values and draws on their Indigenous cultural practices.

Unless the structural inequities and hegemonic practice Pāsifika students encounter in New Zealand schools are addressed, serious social and political consequences are signaled when considering the projected demographics. Vale et al. (2016) highlight how the connection between “educational achievement including aspirations and socio-economic context are predictably consistent” (p. 100). These researchers draw on the work of Jorgensen and her colleagues (2012, 2014) who argue that contributing factors to underachievement include “student mix, student family background, parental connection(s) to school, teacher quality, student language skill(s), curriculum alienation and so on” (p. 100); all factors we see in our work with Pāsifika students. These students are predominantly found in schools within high poverty areas and where socioeconomic disadvantages are the greatest.

Throughout this chapter, we engage with issues of equity and social justice and illustrate how particular practices used in New Zealand schools have marginalized Pāsifika learners and caused many to be disenfranchised from school mathematics, as a consequence delimiting study and career opportunities. We draw on Nieto’s (2002) framing of culture. Within this framework, the culture of the Pāsifika learner can be seen as one which is comprised of dynamic and ever-evolving traditions, social and political relationships, and a world view constructed, shared, and transformed by a group of people who are joined together by a number of factors which include common values, a common history (for example, originating from and being Indigenous to a Pācific Island nation and being immigrants or children of immigrants to another Pacific Island nation – New Zealand), geographic location, language, social class, and religion. In this chapter at the heart of what we describe is a mathematics program which we argue has the potential to be transformative in addressing social justice issues. Through working within the Developing Mathematical Inquiry Communities (DMIC), teachers are able to engage in Pāsifika-focused culturally responsive teaching to support their students to construct a positive and strong mathematical and cultural identity as mathematical learners and doers in New Zealand classrooms.

In the next section, we will outline the development of Developing Mathematical Inquiry Communities (DMIC) program. Throughout the chapter, we will draw on its components to explore and examine the way in which the different parts of DMIC support Pāsifika students to learn and do mathematics which provide equitable outcomes.

The Context of Developing Mathematical Inquiry Communities

The innovative DMIC program was initially developed more than 15 years ago through collaboration with a group of teachers in a school in a high-poverty urban area in Auckland with predominantly Māori and Pāsifika students. Subsequently, a gradual roll out of schools involved in DMIC has resulted in the current involvement of 52 schools (35 schools in West and South Auckland, 8 schools in Porirua, Wellington, 4 schools in Tauranga, 1 in Rotorua and Palmerston North and 4 schools in Christchurch). Altogether, approximately 950 teachers are formally included in the project although throughout New Zealand many other schools have informally joined. The data used in this chapter was drawn from teacher reflections and interviews collected regularly over each school year by independent researchers throughout the past 15 years. The quotes used in this chapter were selected because they reflect views that have been consistently voiced over the duration of the project by teachers involved in the program.

DMIC was designed to address the persistent underachievement of Māori and Pāsifika students, caused by the many structural inequities they had encountered in previous mathematics programs in New Zealand. This included the recent New Zealand Numeracy Development Project (NZNDP) (Ministry of Education 2004) intervention that, though well intentioned, made minimal difference to mathematics education disparities. Within the NZNDP project, all students progressed but Asian and Pākeha students’ achievement was more accelerated, and so the achievement gap widened significantly for Māori and Pāsifika students (Young-Loveridge 2009). While the NZNDP project promoted some good pedagogical practices, it also reflected the taken-for-granted cultural tapestry embedded in New Zealand schooling structures grounded in the dominant middle class Pākeha or “white” culture (Milne 2013). These schooling structures, we will show have allowed deficit theorizing to be maintained towards many Pāsifika learners.

In the next section, we describe the effect of deficit theorizing and how it has contributed to negative teacher and student perceptions of Pāsifika students as mathematical learners.

Causes and Effects of Deficit Theorizing

Consistently over time, the lower educational performance of groups of diverse students, such as Pāsifika peoples within the New Zealand context, has been attributed to the learners themselves or to their impoverished circumstances (Nieto 2002). Deficit theorizing which is applied to those marginalized within the mathematics classroom is immediately evident in teacher reflections when we begin to enact DMIC classrooms within schools with Pāsifika students. Frequently, our initial work with teachers is framed by comments from teachers such as “you don’t understand, these students come to school with no mathematics.” A reflection from a Principal after a year of their school being involved in DMIC noted the influence of deficit theorizing on their expectations:

All of those things that we probably thought that our kids couldn’t do but we weren’t giving them the opportunity to do that.

In this statement the Principal has recognized that learning is enabled or constrained by the opportunities provided to students.

Pāsifika students are similarly influenced by their experiences in New Zealand classrooms. Quotes from them prior to beginning in DMIC classrooms illustrate the deficit views they hold of their own culture in relation to mathematics. When asked “how does it feel to be ____ (here we are exploring their cultural identity) in the mathematics classroom” approximately 20% of student responses indicate a negative view. One perception, often presented, is a view that the cultural or ethnic group they identify with do not engage with mathematics:

Sometimes it makes me feel different because Tokelauans don’t do maths.

Other students indicate a belief that to be successful in mathematics you must enter what Milne (2013) described as “white-space.” This is a space in an educational setting which represents the dominant middle class Pākeha or “white” cultural group:

It feels like I’m a different person from a Samoan person… because whenever I’m learning maths I think I’m a Palagi (White) person… because whenever I’m doing maths I can’t remember I’m Samoan. I don’t like about maths when I get up to the hard part I can’t do it I don’t feel like a white person anymore I feel like myself again and I’m nervous.

In contrast, after a year in DMIC classrooms all students could make connections between both mathematics in their classrooms and mathematics within their Indigenous culture. Moreover, they indicated the relevance of mathematics in their lives. They could also provide a counter to a common perception about who is considered capable in mathematics based on their observations of teacher behavior:

It feels good that your teacher likes (you) cause like sometimes teachers think that like white people and Asian people will get the answer correct but it’s good that our teacher believes in all of us. Like she believes in all of us in the same way and yeah it’s really good.

Many of the common deficit views held by New Zealand teachers and the students themselves can be attributed to the way in which streaming by ability is a common practice in New Zealand schools. Ability grouping has a long history as a popular pedagogical strategy used in mathematics in New Zealand classrooms and its use was further popularized by the New Zealand Numeracy Development Project (Ministry of Education 2004) as a prescribed part of the Project in the form of strategy-based teaching groups (Ministry of Education 2004) and continues to be used in the current Accelerated Learning in Mathematics (ALiM) program. Given that only 11% of Year 8 Pāsifika students are at or above curriculum standards (Education Assessment Research Unit and New Zealand Council for Educational Research 2015), it can be assumed that most Pāsifika learners find themselves in the lower ability groups. We have suggested in previous articles (Civil and Hunter 2015; Hunter and Anthony 2011) that the widespread use of ability grouping as a practice may be another cause for Pāsifika students’ disaffection with mathematics. In the next section, we will elaborate on possible reasons.

Grouping by ability in mathematics classrooms is a contested pedagogical practice. Many supporters of ability grouping argue that it is a means to cater with wide student diversity in classrooms. Although some researchers (e.g., Kulik and Kulik 1992) argue that particularly the gifted and talented students benefit when ability grouped, other researchers (e.g., Braddock and Slavin 1995; Boaler and Wiliam 2001) contend that grouping by ability neither caters for all students nor raises achievement. This was confirmed in a recent PISA study (Scheicher 2014) which indicated that the degree of a school system’s vertical stratification was negatively related to equity of education outcomes, while there was no clear relationship with excellence. The researchers outline limited positive effects on student learning while comparing these with the many negative outcomes (Scheicher 2014). These include development of low self-esteem and disengagement from learning. More importantly, as is the case for our Pāsifika learners, Zevenbergen (2003) outlines how students from the dominant cultural groups often occupy the upper ability groups while students from marginalized groups (for example, low SES, Indigenous, immigrant, and culturally diverse) are most often found in the lower ability groups. Zevenbergen (2003) theorizes that the different ability groupings of students are more a reflection of social constructs than intelligence or ability. What Zevenbergen (2003) suggests and we can confirm happens in New Zealand is that when ability groups are used where different groups of students are positioned is not a random occurrence, rather it is closely linked to student backgrounds and whether their cultural capital (Bourdieu and Passeron 1973) is privileged in the context of the classroom.

Previously (Civil and Hunter 2015; Hunter 2008; Hunter and Anthony 2011) we illustrated the way in which as a group of learners Pāsifika students are often more reticent to talk and are also less likely to ask questions or to challenge. We suggest that this particular cultural behavior is often assumed by teachers to be an indicator of lack of understanding, thus leading erroneously to Pāsifika students being disproportionately represented in the “lower” ability groups in classrooms. Not only does this cultural disconnect lead to poor judgments on behalf of the teacher but also the use of ability-based teaching groups in themselves is contrary to the values and ethos of Pāsifika learners and whānau (the extended family or community who live together in the same area). The use of streamed groups encourages undesirable competitiveness and places an importance on individual success. An emphasis or focus on the individual is in direct contrast to the Pāsifika notions of the value of communalism and collectivism. Within a Pāsifika view, the success of individual group members is judged by the success of the collective as a whole. Within this frame, the role of the individual includes being of service to others and within the mathematics context the focus is on ensuring that the knowledge is constructed and shared collectively. Integrating Pāsifika values into the DMIC environment is also reflected in how the Pāsifika students view what doing mathematics encompasses. They integrate being successful as a mathematical learner within a positive cultural identity. This is illustrated by a student in a DMIC classroom who compared her former experience in a high-ability group in a previous classroom with her current experience in a mixed ability group in a DMIC classroom:

At the start of the year I would have said being a successful mathematician meant being in the top group and getting the answers right. Now, I think it is being a good person. Not being the person who is always right but helping others as well. That makes you good at maths.

A number of researchers (e.g., Boaler et al. 2000; Marks 2012; Zevenbergen 2001) describe the qualitatively different experiences learners have from each other in the ability-grouped classrooms, and the way in which teacher expectations of different groups of mathematical learners widened the gap between them rather than affording all students the same learning and growth opportunities. This can be explained when you consider that there is a tendency for students in higher ability groups to receive rich and challenging learning experiences while the students in the lower groups are most often likely to receive more procedural teaching shaped around lower expectations (Boaler 2014). A common reflection we hear from teachers after their initial introduction to DMIC is illustrated in this teacher’s statement:

I am really surprised when I hear some of the kids I thought were lowies asking good questions or sharing their thinking, really good thinking…I really thought they knew nothing and so I just used to tell them what to do.

Her beliefs about the perceived ability of the students in the lower groups had formed the basis of her deficit thinking and shaped her expectations for what they could say or do. In contrast towards the end of the year we see shifts in beliefs, and many teachers voice similar thoughts to the teacher here:

Hmm- I never thought my children couldn’t do mathematics but I’m enjoying exposing all children to bigger number, decimals etc. I have had some surprises when listening to children share strategies, very exciting when you would never have heard it in the past. When the passive, quiet ones speak it is a magical moment.

A consistent theme across the different teachers is a level of surprise and excitement at what happens when all children are provided with learning opportunities that are challenging and culturally meaningful to them. However, what the students are getting is access to learning opportunities that similarly develop a positive mathematics identity afforded to other students in New Zealand classrooms.

In the next section we will outline the components central to DMIC and to developing students with a strong and positive mathematical identity.

The Components of Developing Mathematical Inquiry Communities

DMIC incorporates the best pedagogical practices of what has been termed variously as inquiry or reform (Wood et al. 2006) or ambitious mathematics teaching (Kazemi et al. 2009) within culturally responsive teaching (Gay 2010). The focus of DMIC is on development of in-school and across-schools collaboration in building classroom communities of mathematical inquiry. A key part of the DMIC mathematics program are the participation and communication patterns that support students to construct and use proficient and reasoned mathematical practices (Hunter 2008). Central to the DMIC work is a Communication and Participation Framework (Hunter 2008); a tool used to scaffold teachers to engage students in mathematical practices within communities of mathematical inquiry. An important component of the Communication and Participation Framework is the ways in which teachers can use it adaptively, flexibly, and in culturally responsive ways.

The development of proficient mathematical practices is closely aligned to construction of a positive mathematical identity. Although there are inconsistencies in the use of the term identity in mathematics education, some researchers (e.g., English et al. 2008; Gutiérrez 2013; Sfard and Prusak 2005) draw our attention to the way in which mathematical identities are developed through engagement and participation in mathematical activity. For example, identity has been referred to by Sfard and Prusak (2005) as the “missing link” in the “complex dialectic between learning and its sociocultural context” (p. 15). Other researchers draw our attention to the way in which identity is related to issues of power (Gutiérrez 2013) and access (English et al. 2008) and therefore to equity concerns. Considering mathematical identity as developed within mathematical activity in turn highlights the importance of all students being provided with opportunities to participate in mathematical practices.

Mathematical practices evolve through socially constructed interactive discourse. They are specific to, and encapsulated within, the practice of mathematics (Ball and Bass 2003). Mathematical practices include the mathematical know-how which extends beyond constructing mathematical knowledge to include specific actions and ways of learning and using mathematics. There are many examples of mathematical practices which proficient problem solvers use and do and these include explaining, representing, and “justifying claims, using symbolic notation efficiently, defining terms precisely, and making generalizations [or] the way in which skilled mathematics users are able to model a situation to make it easier to understand and to solve problems related to it” (RAND 2003, p. xviii). Inherent in the development and use of mathematical practices are specific ways of talking and reasoning, ways of asking questions, and challenging others.

To engage students in mathematical practices can be challenging for a number of reasons. As noted, not all students are comfortable asking questions or explaining their reasoning beyond talking to a friend. The challenges were illustrated through interviews at the beginning of the school year when the students had just begun in DMIC classrooms. In the early interviews, a substantial number (46%) of the students gave negative responses when asked about engaging in mathematical practices (for example, explaining and justifying mathematical explanations, representing reasoning, and responding to challenge). Their initial responses were often linked to emotional aspects (e.g., being scared, or feeling nervous, or frightened). The responses were also commonly associated with negative behavior from peers such as being laughed at or ridiculed. For example, one student stated:

What I don’t like about math is about how when you make a mistake people make a big joke out of it and then that can be really embarrassing.

Similarly, another student when asked about explaining their ideas said:

I feel kind of nervous because sometimes other people might say no that’s wrong and it freaks me out… because it feels like I’ve done everything wrong.

At the end of the year, after the students had been in the DMIC classrooms, there was a noticeable shift in the student attitudinal/emotional responses; considerably fewer students (13%) provided a negative response. Interestingly, the negative responses were no longer linked to derogatory responses from peers; rather they were personal characteristics linked to self-descriptions of themselves as shy or quiet:

(I don’t like) Getting up and showing my work because I’m nervous around people… I’m a quiet kid.

Developing a classroom in which students use a range of mathematical practices within a community of inquiry is challenging for many teachers, whether working with students from the dominant middle class Pākeha or more diverse groups (Hunter 2010). The complexities are many, including who talks when and how, and what mathematics is talked about (Hunter 2008). In this program, teachers are required to reposition themselves as facilitators and members of the learning community (Hunter 2013) and engage students in constructing and presenting mathematical explanations and justification. Providing equitable access for all students to participate in the mathematics discourse of the learning experience substantially increases the demand on teachers to understand the culture of their students. This is illustrated in reflections made by teachers when they have just begun to engage in the DMIC program. For example, one teacher wrote the following statement:

Challenged by establishing the idea of our learning waka [canoe]; a culture of learning together to succeed, I was surprised at how little I knew about my students. I have had to really talk to the children like what they do on weekends and special times and ask the Pāsifika teachers about food they eat.

Nevertheless, many teachers are open to change when they explore the possibilities. As an example one teacher stated:

Cultural-cognitive link opens up a raft of issues that stereotype Pāsifika as a disadvantaged segment of society. The new maths strategy will enable real growth to be made, with the greatest benefactor being me!

When teachers take into account Pāsifika languages, cultures, and identities, the mathematics teaching pedagogy in the schooling context changes, and the students are more readily able to engage in mathematical practices. This is consistent with what we have learnt from Paulo Freire (2000) about transformative education. Freire argues that through engaging people who have been marginalized and dehumanized by drawing on what they already know, education is able to transform oppressive structures in equitable ways. Within DMIC classrooms, careful consideration is given to increasing student voice and autonomy to question and challenge in culturally appropriate ways. In a previous article Hunter and Anthony (2011), drawing on findings from a DMIC classroom, illustrated that when the teacher attended to classroom social and discourse norms, more students were able to engage and contribute at higher cognitive levels. In particular, what was highlighted was how participation increased in mathematical practices and activities when the teacher considered his or her Pāsifika students’ strengths and employed pedagogical strategies constructed around the Pāsifika values, and when they provided space which was “culturally, as well as academically and socially responsive” (MacFarlane 2004, p. 61).

Other aspects of the DMIC program include a demand for teachers to have high expectations and use challenging contextualized tasks , which are more likely to lead to rich conceptual understandings. The problems and tasks are set within the known and lived social and cultural reality of the students. Careful consideration is given to how the students view their ways of participating and communicating. The intent is that they are able to maintain their cultural identity while simultaneously building a positive mathematical identity. Social norms which shape classroom work and interactions are built around core Pāsifika values in order to ensure that our Pāsifika students are able to participate fully in mathematical practices.

Pāsifika Values and Their Role in Shaping Classroom Social Norms

Given the increased emphasis over the past two decades placed on the students communicating their mathematical reasoning, equitable participation in the mathematical discourse is of prime importance and Pāsifika values play a central role (Hunter 2007). Although the Pāsifika students in DMIC classrooms are composed of a diverse group of Pācific Nations people, together they have a set of cultural commonalities. These are within a set of core Pāsifika values which include such values as reciprocity, respect, service, inclusion, family, relationships, spirituality, leadership, collectivism, love, and belonging (Anae et al. 2001). Pāsifika students in the classrooms may be first generation to New Zealand or they may be second, third, or even fourth generation New Zealand born and may be variously influenced by the majority cultural norms. Nevertheless, the core Pāsifika values of their whānau continue to have a major impact on how they interact and behave within their home and affect how they participate and communicate in the school context.

Core Pāsifika values can cause dissonance for some Pāsifika students because they do not align with those commonly used in New Zealand classrooms. Bok (2010) suggests educational systems tend to privilege the beliefs and values of the dominant middle class. This dissonance was illustrated by Hunter and Anthony (2011) where they found that the Pāsifika students on entry to a DMIC classroom indicated that they considered they learnt through listening to the teacher as an appropriate mode of learning. Notions of listening (rather than active participation and inquiry) links to the Pāsifika value of respect where teachers as elders are considered to hold knowledge which is always correct and unquestionable. Similarly, they illustrated the discomfort Pāsifika students initially felt when required to question and challenge the teacher and other students, because they were concerned that it might be considered disrespectful and could cause a loss of face. Learning mathematics is about learning the codes of the discipline of mathematics including how to engage in a range of mathematical practices including argumentation. Clearly if, as Gutiérrez (2002) argues, we need to consider the importance of participation and achievement (as learning) we need to think about how the Pāsifika values can be placed at the center of teachers’ practices to support students to engage in mathematics.

School mathematics is not just about learning mathematics knowledge; it is also about learning to engage in particular behavior and act like a mathematician. As part of challenging the hegemonic European practices commonly found in many New Zealand classrooms, within the DMIC program we enact what Atweh and Ala’i (2012) term a “socially response-able approach to mathematics education ” (p. 98). Rather than using direct instruction, the teachers use more open and flexible pedagogy which incorporates the core Pāsifika values to shape the social norms of the classroom. The students work in small groups to construct shared problem solutions. Clear expectations are placed on them that they have both an individual responsibility to understand and a collective responsibility that they make sure their peers understand also. As part of the interactions in the classroom, notions of working as a family are emphasized because family, particularly the extended family, encompasses all the Pāsifika values. As one teacher explained:

Family is big, it’s everything. The way our classes are set up now everyone has a chance to share ideas, and like a family everyone helps out, and nobody is left out because everybody has a job to do and that’s the Pāsifika way and the Māori way. We talk about that a lot as a class, like if you are doing the housework everybody helps or if you are making an umu or hangi (earth oven) everybody has a job to do. It might be dig the hole or peel the spuds but you have a job… and like with a vaka (canoe) everybody has got to paddle in the same direction, in time if you are going to move and the kids can relate to that because that’s their world.

In turn, the students talk about their place in these classrooms in ways which reveal their sense of relationships, family, and belonging. It is evident that drawing on the common values of the different cultural groups represented in Pāsifika peoples, being responsive to “students’ cultural ways of being” (Civil and Hunter 2015, p. 296) and using these to shape the social norms support the students to construct a positive mathematical and cultural identity.

Connecting Mathematical Problems to the World of the Students

Central to growing our Pāsifika students’ mathematical understandings as rich conceptual knowledge is the use of group-worthy (Featherstone et al. 2011), mathematically complex and challenging problems or problematic activity. A requirement in the construction of the problems is the need for connections to be made with the cultural and social contexts of the students’ daily lives. This undoubtedly poses challenges for teachers as this teacher explains:

The challenge is making things culturally relevant when I don’t have the cultural knowledge myself so I find myself tending to write problems about school life, fruit, sport, gear, etc.

The emphasis in the writing of the problems is on the world the students currently inhabit in their beyond school world where they locate themselves. This allows for the students to recognize and value mathematics in their social and cultural world and gain access to the mathematics in the problem. In New Zealand, the school mathematics problems, activities, and pedagogy have most often better reflected the cultural capital of the dominant middle class Pākeha cultural groups. In this chapter, the term cultural capital used by Bourdieu and Passeron (1973) is defined by McLaren (1994) as being the general cultural background, knowledge, disposition, and skills that are passed on from one generation to another. As we use it, cultural capital represents “ways of talking, acting, and socialising, as well as language practices, values, and types of dress and behaviour” (McLaren 1994, p. 219). The act of teachers writing specific problems around the world of Pāsifika students repositions them as having valid cultural capital in their own mathematics classrooms as is evident in the following student statements:

The maths is about us, about the community. The problems relate to our cultures and celebrations which makes it more understandable.

It makes it easier for us to learn…like the ula lole (lolly necklace) problem because most of us have made it before and we can see it and have a picture in our minds so we can see how it’s proportions and ratios like one chocolate to three fruit burst or minties.

Their responses illustrate their recognition that the activities that they engage in at home involve mathematics and that it is valued. Moreover, having the problems set within contexts they can relate to makes the mathematics more accessible. As Freire (2000) argues, to gain equitable outcomes, it is important to situate educational activity in the lived experience of the learners.

Language and Cultural Identity

In New Zealand we have had a long history in education of “English language only” policies, both overt and covert. Although government policy changed more than 30 years ago with the renaissance of Māori in the 1970s, many teachers still hold implicit beliefs that students should speak in English at school and English remains the language of instruction (Meaney 2013). Many Pāsifika students enter New Zealand schools fluent in their own language and with a rich background of knowledge and experiences, but within a short period of schooling they join the disproportionately high numbers of Pāsifika students who are failing within our current education system. Language-based equity issues are a constraining factor. Within DMIC classrooms, teachers are asked to support students to shift between their first home language and English when discussing, explaining, and justifying their mathematical understandings. This acknowledges the difficulties Pāsifika students encounter when learning mathematics including when equivalent words or concepts are not readily available in their first language. The word problems used in DMIC classrooms require that the students read and make sense of the problem contexts. The ability to code-switch from one language to another to support student understandings thus provides equitable access. Initially some teachers voice concerns that they do not know what the students are saying when they encourage students to use both languages; however, they come to realize it is an important consideration in the empowerment of the students. For example, two different teachers explained why it was needed:

I am Samoan so I understand what they are saying as well but if they were Cook Island I would just get some of the Cook Islanders to talk in their language and translate for me or represent in a different way so I would get them to draw it and I would understand what they are drawing so it doesn’t matter what nationality they are.

It’s really powerful if they can use their own language because sometimes it might just be that they don’t understand the question or even the ones that speak English there might not be a word in English that represents what they are talking about or they might be more confident speaking Samoan or Tongan and then others can translate. Without that, like in the past those kids didn’t have a voice and you would just think they couldn’t do it. It really helps transfer the power as well, as I don’t always understand and they have to translate for me and their understanding really improves when they do this.

Clearly, the teacher had recognized that speaking in a language the student chooses supported the development of student voice and agency. In student interviews, the students also acknowledged how speaking in their first language provided opportunities for their peers. At the same time, it normalized their use of their first language within the school environment and added to their cultural identity (and mathematical identity):

Sometimes it helps to explain things in Tongan because some of the Tongans in our class are new and their English isn’t that good but they can understand the maths in Tongan which is cool because before you didn’t really speak Tongan in class.

Language is closely interwoven with culture and identity for Pāsifika students. Clearly evident in the DMIC classrooms is the way in which the use of the student’s first language supports them as learners to draw on the Pāsifika values in ways which they feel comfortable. Other studies in DMIC classrooms (e.g., Bills and Hunter 2015; Civil and Hunter 2015; Hunter and Anthony 2011) show that when teachers use pedagogy situated within the known world of their Pāsifika students, and which premise student choice over the spoken language they use, achievement results are reversed, and positive cultural identities and mathematical dispositions are constructed. Evident in these studies is recognition that mathematics education is a sociocultural activity embedded in sociopolitical contexts with the teaching and learning of mathematics as “situational, contextual and personal processes” (Taylor and Sobel 2011, p. ix).

High Expectations and Ethics of Care

While teachers in our program commonly state that they think all children can do mathematics, the way they phrase these statements belies the spoken words and indicates that they hold fixed mind sets (Dweck 2008). Fixed mind sets are exemplified when teachers are continuously influenced by theories which relate to grouping and teaching by ability and which support deficit thinking which we will explore later in this chapter. Dweck (2008) argues a need for teachers to hold a growth mind set: one in which ability is not fixed but able to be grown and changed. Within a growth mind set, mathematical ability is grown through persistence, effort and hard work, challenges and struggle are celebrated, and mistakes are considered learning opportunities. Dissonance supports the development of a growth mind set as is evident in the following teacher statement:

This is all hard learning for me. I am implementing more effectively the justification status, intellectual contribution ideas. I believe this is instrumental in not only improving learning across all areas for all students, but also in solving problems I am having with a group of boys. I think they are having mind-set difficulties and won’t take risks because their maths knowledge they think is low.

Closely tied to a growth mind set is that of notions of ethics of care. An ethic of care is an important component of the mathematics classroom (Noddings 2005). A lot of importance is placed on how to enact ethics of care in ways which enable rather than disable students. At times, an ethic of care may be misinterpreted by teachers. For example, rather than encouraging students to risk-take and celebrate mistakes, at times teachers think that they should keep the students safe from mathematical practices because they may make them feel uncomfortable. As noted, we reported earlier about the reluctance of some Pāsifika students to talk or ask questions during classroom lessons. Some teachers respond by allowing the behavior, misunderstanding and interpreting it as a Pāsifika trait. However, as a key equitable action, the teachers need to interpret and work with the behavior within an ethic of care. Within this frame they need to draw on the Pāsifika values to scaffold students to engage in the mathematical discourse. Such actions indicate that they care enough to facilitate a student to engage in essential mathematical practices within culturally responsive environments. Drawing on ethics of care can be challenging for teachers and so, initially, they have to explore ways to enact it. But once the teachers realize its importance, it becomes a feature of their practice and a way to increase their expectations of all students. As an example, here is a quote from a teacher who realized the power of using an ethic of care in a culturally responsive way:

I challenged the children to explain their thinking so I could see what they were capable of, and what a difference it made. I saw how well the children responded too and how much they enjoyed the challenging questions they were asked.

Pāsifika students can also step in and “save” their peers as part of them enacting the Pāsifika values. Nevertheless, teachers need to consciously support them to work within an ethic of care and support students in a different way. For example, one teacher described a boy from her classroom as easily missed during small group work because he never spoke and did not participate. She observed that the other students in his group would “save” him by providing an answer for him. She went on to describe her actions during small group-work:

I just said “Oh no, remember we care about Tane enough that we want to hear what he has to say. If he doesn’t know then he knows what he needs to do to ask. You know that he needs to ask a question.”

She then went on to describe how after a long period of waiting, the student asked a question. He then responded and the pride which resulted from his participation was evident for all to see.

Conclusion

Notions of equity are a complex and challenging concept within mathematics education. To some, equity in mathematics education is equated as equal opportunities for all to learn through accessing both a common mathematics curriculum and qualified teachers; others equate equity with equality of mathematical achievement outcomes across student groups (Foote and Lambert 2011). However, Gutiérrez and Dixon-Román (2011) argue the need to look beyond taking what they term interchangeably as either “gap gazing” or an “achievement gap perspective” (p. 23). They call attention to the problems which emerge because this lens supports an assimilationist approach in which the aim is to close the gap between students from the dominant culture (in New Zealand the middle class Pākeha students represented in the hegemonic European practices) and the marginalized students, in contrast to questioning the validity of the measurement tools or even the focus on achievement. This assimilationist approach is represented in the New Zealand Ministry of Education requirements which focus mainly on our reporting of lifts in achievement according to the national standards. Although, lifts in student achievement have been part of the success of DMIC, the more important focus has been on other valued outcomes including an increase in student voice and agency, increased pro-social skills, enhanced mathematical dispositions, and the valuing of the mathematics within the home and cultural context. For example, when interviewed a number of students made reference to their increased autonomy:

In this maths we have more power. He [teacher] gives us the problem but the problem is about us …. Our reality and we have to figure it out, we are responsible for our own learning and others’ learning too, we have control.

Other students talked about how being taught mathematics in a DMIC classroom normalized them and their culture within the school setting:

When the maths is about us and our culture, it makes me feel normal, and my culture is normal.

Yeah like it is normal to be Samoan or Tongan.

However, these important outcomes are not positioned within the New Zealand education system as being valued outcomes and as a result “gap gazing” prevails.

We argue that the achievement gap discourse diverts attention away from the structural inequities Pāsifika students encounter in many mathematics classrooms and by failing to question these, the prevailing discourse of “gap gazing” puts the problem back with the Pāsifika community. In this way, the disengagement of Pāsifika students from mathematics can be attributed to constructs other than the teacher and is attributed to factors including personal and psychological, home environments and poverty. Other researchers (e.g., Delpit 1988; Flores 2007; Ladson-Billings 2006; Martin 2007; Milne 2013) frame equity issues around various alternative gaps. These include the power gap, the opportunity gap, the education debt, and the white spaces created when the hegemonic European practices dominate the curriculum. These have all been evident in the different sections of this chapter.

Bok (2010) draws our attention to the way in which educational systems are significant in the reproduction of unequal access to, and results from, education systems for such students from high poverty areas. In contrast to those more economically privileged, they do not have the requisite social and cultural capital (Bourdieu and Passeron 1973) that positions them for success in school and beyond. Vale et al. (2016) point out the ways in which schools reflect certain pedagogical practices. They describe how mathematics teaching is particularly “susceptible to routinized practice” (p. 100) in which teacher voice dominates. Unfortunately, this leads to issues of social justice because evidence shows that teachers adjust their teaching approaches and expectations to their perceptions of what they consider students are capable of (Atweh et al. 2014). Issues of social justice were evident throughout the chapter.

In this chapter we have drawn on 15 years of on-going research in New Zealand mathematics classrooms. We have illustrated that the teaching and learning of mathematics cannot be decontextualized based on the pervasive public belief that mathematics is “culture-free”; a view which supports the cultural deficit or “cultural blindness” (Gay 2010, p. 21) paradigm taken by many New Zealand educationalists. Our focus has been placed on the many different components of Pāsifika-focused culturally responsive teaching and the journey teachers in schools with predominantly Pāsifika students take to enact it. While the journey to develop a mathematics learning environment in which Pāsifika students are able to construct both a strong and positive cultural and mathematical identity is challenging, the words of a teacher say it all:

The Project is using the strengths of our Pāsifika whānau and children to improve their maths and to achieve.

References

  1. Alton-Lee A (2003) Quality teaching for diverse students in schooling: best evidence synthesis. Ministry of Education, WellingtonGoogle Scholar
  2. Anae M, Coxon E, Mara D, Wendt-Samu T, Finau C (2001) Pāsifika education research guidelines. Ministry of Education, WellingtonGoogle Scholar
  3. Atweh B, Ala’I K (2012) Socially response-able mathematics education: lessons from three teachers. In: Dindyal J, Cheng LP, Ng SF (eds) Mathematics education: expanding horizons. Proceedings of the 35th annual conference of the Mathematics Education Research Group of Australasia, vol 1. MERGA, Singapore, pp 99–105Google Scholar
  4. Atweh B, Bose A, Graven M, Subramanian J, Venkat H (2014) Teaching numeracy in numeracy and early grades in low income countries. Gmbn Deutsche. Available via https://www.giz.de/expertise/downloads/giz2014-en-studie-teaching-numeracy-preschool-early-grades-numeracy.pdf. Accessed 20 Nov 2016
  5. Ball D, Bass H (2003) Making mathematics reasonable in school. In: Kilpatrick J, Martin J, Schifter D (eds) A research companion to the principles and standards for school mathematics. National Council of Teachers of Mathematics, Reston, pp 27–45Google Scholar
  6. Bills T, Hunter R (2015) The role of cultural capital in creating equity for Pāsifika learners in mathematics. In: Marshman M, Geiger V, Bennison A (eds) Mathematics education in the margins. Proceedings of the 38th annual conference of the Mathematics Education Research Group of Australasia. MERGA, Sunshine Coast, pp 109–116Google Scholar
  7. Boaler J (2014) Ability grouping in mathematics classrooms. In: Lerman S (ed) Encyclopedia of mathematics education. Springer, Dordrecht, pp 1–5Google Scholar
  8. Boaler J, Wiliam D (2001) ‘We’ve still got to learn’. Students’ perspectives on ability grouping and mathematics achievement. In: Gates P (ed) Issues in mathematics teaching. RoutledgeFalmer, London, pp 77–92Google Scholar
  9. Boaler J, Wiliam D, Brown M (2000) Students’ experiences of ability grouping – disaffection, polarisation and the construction of failure. Br Educ Res J 26(5):631–648CrossRefGoogle Scholar
  10. Bok J (2010) The capacity to aspire to higher education: “it’s like making them do a play without a script”. Crit Stud Educ 5(2):163–178CrossRefGoogle Scholar
  11. Bourdieu P, Passeron JC (1973) Cultural reproduction and social reproduction. In: Brown RK (ed) Knowledge, education and cultural change. Tavistock, LondonGoogle Scholar
  12. Braddock J, Slavin R (1995) Why ability grouping must end: achieving excellence and equity in American education. In: Pool H, Page J (eds) Beyond tracking: finding success in inclusive schools. Phi Delta Kappa Educational Foundation, Bloomington, pp 7–20Google Scholar
  13. Brown T, Devine N, Leslie E, Paiti M, Sila’ila’i E, Umaki S, Williams J (2007) Reflective engagement in cultural history: A Lacanian perspective on Pāsifika teachers in Aotearoa New Zealand. Pedagog Cult Soc 15(1):107–118CrossRefGoogle Scholar
  14. Civil M, Hunter R (2015) Participation of non-dominant students in argumentation in the mathematics classroom. Intercult J 26(4):296–312CrossRefGoogle Scholar
  15. Delpit LD (1988) The silenced dialogue: power and pedagogy in educating other people’s children. Harv Educ Rev 58(3):280–298CrossRefGoogle Scholar
  16. Dweck C (2008) Mindset and math/science achievement. Teaching & leadership: managing for effective teachers and leaders. www.opportunityequation.org
  17. Education Assessment Research Unit and New Zealand Council for Educational Research (2015) Wānangatia te Putanga Tauira National monitoring study of student achievement: mathematics and statistics 2013. Ministry of Education, WellingtonGoogle Scholar
  18. English LD, Jones GA, Bartolini Bussi M, Lesh RA, Tirosh D, Sriraman B (2008) Moving forward in international mathematics education research. In: English LD (ed) Handbook of international research in mathematics education, 2nd edn. Routledge, New York, pp. 872–905Google Scholar
  19. Featherstone H, Crespo S, Jilk L, Oslund J, Parks A, Wood M (2011) Smarter together! Collaboration and equity in the elementary math classroom. NCTM, RestonGoogle Scholar
  20. Flores A (2007) Examining disparities in mathematics education: achievement gap or opportunity gap? High Sch J 91(1):29–42CrossRefGoogle Scholar
  21. Foote MQ, Lambert R (2011) I have a solution to share: learning through equitable participation in a mathematics classroom. Can J Sci Math Technol Educ 11(3):247–260CrossRefGoogle Scholar
  22. Freire P (2000) Pedagogy of the oppressed. Continuum, New YorkGoogle Scholar
  23. Gay G (2010) Culturally responsive teaching: theory, research and practice. Teacher’s College Press, New YorkGoogle Scholar
  24. Gutiérrez R (2002) Enabling the practice of mathematics teachers in context: toward a new equity research agenda. Math Think Learn 4(2/3):145–187CrossRefGoogle Scholar
  25. Gutiérrez R (2013) The sociopolitical turn in mathematics education. J Res Math Educ 44(1):37CrossRefGoogle Scholar
  26. Gutiérrez R, Dixon-Román E (2011) Beyond gap gazing: how can thinking about education comprehensively help us (re)envision mathematics education? Springer, DordrechtGoogle Scholar
  27. Hunter R (2007) Teachers developing communities of mathematical inquiries. Unpublished doctoral thesis, Massey University, Palmerston NorthGoogle Scholar
  28. Hunter R (2008) Facilitating communities of mathematical inquiry. In: Goos M, Brown R, Makar K (eds) Navigating currents and charting directions. Proceedings of the 31st annual conference of the Mathematics Education Research Group of Australasia, vol 1. MERGA, Brisbane, pp 31–39Google Scholar
  29. Hunter R (2010) Changing roles and identities in the construction of a community of mathematical inquiry. J Math Teach Educ 13(5):397–409CrossRefGoogle Scholar
  30. Hunter R (2013) Developing equitable opportunities for Pasifika students to engage in mathematical practices. In: Lindmeier AM, Heinze A (eds) Proceedings of the 37th international group for the psychology of mathematics education, vol 3. PME, Kiel, pp 397–406Google Scholar
  31. Hunter R, Anthony G (2011) Forging mathematical relationships in inquiry-based classrooms with Pasifika students. J Urban Math Educ 4(1):98–119Google Scholar
  32. Jorgensen R (2012) Exploring scholastic mortality among working class and Indigenous students: a perspective from Australia. In: Herbel-Eisenmann B, Choppin J, Wagner D, Pimm D (eds) Equity in discourse for mathematics education: theories, practices and policies. Springer, Dordrecht, pp 35–49CrossRefGoogle Scholar
  33. Jorgensen R, Gates P, Roper V (2014) Structural exclusion through school mathematics. Educ Stud Math 87(2):1–19CrossRefGoogle Scholar
  34. Kazemi E, Franke M, Lampert M (2009) Developing pedagogies in teacher education to support novice teachers’ ability to enact ambitious instruction. In: Hunter R, Bicknell B, Burgess T (eds) Crossing divides, proceedings of the 32nd annual conference of the Mathematics Education Research Group of Australasia. MERGA, Wellington, pp 11–29Google Scholar
  35. Kulik J, Kulik C (1992) Meta-analytic findings on grouping programmes. Gift Child Q 36(2):73–76CrossRefGoogle Scholar
  36. Ladson-Billings G (2006) From the achievement gap to the education debt: understanding achievement in U.S. schools. Educ Res 35(7):3–12CrossRefGoogle Scholar
  37. Lampert M, Beasley H, Ghousseini H, Kazemi E, Franke M (2010) Using designed instructional activities to enable novices to manage ambitious mathematics teaching. In: Stein MK, Kucan L (eds) Instructional explanations in the disciplines. Springer, Pittsburgh, pp 129–141CrossRefGoogle Scholar
  38. MacFarlane A (2004) Kia hiwa ra! Listen to culture. New Zealand Council for Educational Research, WellingtonGoogle Scholar
  39. Marks R (2012) How do children experience setting in primary classrooms? Math Teach 230:5–8Google Scholar
  40. Martin D (2007) Mathematics learning and participation in African American context: the co-construction of identity in two intersecting realms of experience. In: Nasir N, Cobb P (eds) Diversity, equity, and access to mathematical ideas. Teachers College Press, New York, pp 146–158Google Scholar
  41. McLaren P (1994) Life in schools: an introduction to critical pedagogy in the foundations of education. Longman, New YorkGoogle Scholar
  42. Meaney T (2013) The privileging of English in mathematics education research, just a necessary evil? In: Berger M, Brodie K, Frith V, Le Roux K (eds) Proceedings of the seventh international mathematics and society conference, vol 1. MES7, Cape Town, pp 65–84Google Scholar
  43. Milne A (2013) Colouring in the white spaces: reclaiming cultural identity in whitespace schools. An unpublished doctoral thesis, Waikato UniversityGoogle Scholar
  44. Ministry of Education (2004) Book 3: getting started. Learning Media, WellingtonGoogle Scholar
  45. Nakhid C (2003) “Intercultural” perceptions, academic achievement, and the identifying process of Pācific Islands students in New Zealand schools. J Negro Educ 72(3):297–317CrossRefGoogle Scholar
  46. Nieto S (2002) Language, culture, and teaching: critical perspectives for a new century. Lawrence Erlbaum, MahwahGoogle Scholar
  47. Noddings N (2005) The challenge to care in schools. Teachers College Press, New YorkGoogle Scholar
  48. RAND Mathematics Study Panel (2003) Mathematical proficiency for all students: towards a strategic research and development program in mathematics education. RAND, Santa MonicaGoogle Scholar
  49. Scheicher A (2014) Equity, excellence & inclusiveness in education: policy lessons from around the world. International summit on the teaching profession. OECD Publishing. Available via http://dx.doi.org/10.787/978964214033-en. Accessed 2 Nov 2016
  50. Sfard A, Prusak A (2005) Telling identities: in search of an analytic tool for investigating learning as a culturally shaped activity. Educ Res 34(4):14–22CrossRefGoogle Scholar
  51. Taylor SV, Sobel DM (2011) Culturally responsive pedagogy: teaching like our students’ lives matter. Emerald Group Publishing, BingleyCrossRefGoogle Scholar
  52. Vale C, Atweh B, Averill R, Skourdoumbis A (2016) Equity, social justice and ethics in mathematics education. In: Makar K, Dole S, Visnovska J, Goos M, Bennison A, Fry K (eds) Review of Australasian mathematics education research 2012–2015. Sense Publishers, Singapore, pp 97–118Google Scholar
  53. Wendt-Samu T (2006) The ‘Pāsifika umbrella’ and quality teaching: understanding and responding to the diverse realities within. Waikato J Educ 12:35–49Google Scholar
  54. Wood T, Williams G, McNeal B (2006) Children’s mathematical thinking in different classroom cultures. J Res Math Educ 37(3):222–255Google Scholar
  55. Wylie C (2003) Status of educational research in New Zealand: New Zealand country report. New Zealand Council for Educational Research, WellingtonGoogle Scholar
  56. Young-Loveridge J (2009) Patterns of performance and progress of NDP students in 2008. In: Findings for the New Zealand numeracy development project 2008. Ministry of Education, Wellington, pp 12–26Google Scholar
  57. Zevenbergen R (2001) Is streaming an equitable practice? Students’ experiences of streaming in the middle years of schooling. In: Bobis J, Perry B, Mitchelmore M (eds) Numeracy and beyond. Proceedings of the 24th annual conferences of Mathematics Research Group of Australasia. MERGA, Sydney, pp 563–570Google Scholar
  58. Zevenbergen R (2003) Ability grouping in mathematics classrooms: a Bourdieuian analysis. Learn Math 23(3):5Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2017

Authors and Affiliations

  1. 1.Massey UniversityAucklandNew Zealand

Section editors and affiliations

  • Margie Hohepa
    • 1
  • Carl Mika
    • 2
  1. 1.University of WaikatoHamiltonNew Zealand
  2. 2.University of WaikatoHamiltonNew Zealand

Personalised recommendations